# Variation / Proportional

**Direct Variation / Directly Proportional**

*y*is directly proportional to

*x*,

*y*∝

*x*:

$y = kx$

*k* = constant of proportionality*y* varies directly as *x* is another statement equivalent to the above statement.

**Inverse Variation / Directly Proportional**

*y*is inversely proportional to

*x*,

*y*∝ 1/

*x*:

$y = \dfrac{k}{x}$

*k* = constant of proportionality*y* varies inversely with *x* holds the same meaning as the sentence above.

**Joint Variation / Jointly Proportional**

*y*is directly proportional to

*x*and

*z*:

$y = kxz$

*y* is directly proportional to *x* and inversely proportional to *z*:

$y = \dfrac{kx}{z}$

*k* = constant of proportionality

**Variation to n^{th} power of x and m^{th} power of z**

*y*is directly proportional to the square of

*x*and varies inversely to the cube of

*z*:

$y = \dfrac{kx^2}{z^3}$

*k* = constant of proportionality